Home
Class 10
MATHS
If x=asectheta+btantheta and y=atantheta...

If `x=asectheta+btantheta` and `y=atantheta+bsectheta` ,prove that : `x^2-y^2=a^2-b^2`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    RD SHARMA ENGLISH|Exercise All Questions|366 Videos

  • TRIGONOMETRIC RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|249 Videos

Similar Questions

Explore conceptually related problems

If acostheta+b sintheta=x and asintheta-bcostheta=y prove that a^2+b^2=x^2+y^2

If x=asintheta and y=btantheta, then prove that (a^2)/(x^2)-(b^2)/(y^2)=1

If x/a costheta+y/b sintheta=1 and x/a sintheta-y/bcostheta=1 Prove that : (x^2)/(a^2)+(y^2)/(b^2)=2

If x=asectheta , y=btantheta , prove that (d^2y)/(dx^2)=-(b^4)/(a^2\ y^3) .

If a+btantheta=secthetaand b-atantheta=3sectheta , then findthe value of a^2+b^2 .

If (asectheta;btantheta) and (asecphi; btanphi) are the ends of the focal chord of x^2/a^2-y^2/b^2=1 then prove that tan(x/a)tan(phi/2)=(1-e)/(1+e)

If x=asectheta,y=btantheta,"prove that"(d^2y)/(dx^2)=-(b^4)/(a^2y^3)

If x=asectheta and y=btantheta , then b^2x^2-a^2y^2= (a) a b (b) a^2-b^2 (c) a^2+b^2 (d) a^2b^2

If x+i y=(a+i b)/(a-i b) prove that x^2+y^2=1

If x + i y =(a+i b)/(a-i b), prove that x^2+y^2=1 .

RD SHARMA ENGLISH-TRIGONOMETRIC IDENTITIES-All Questions
  1. Prove the trigonometric identities: If Tn=sin^ntheta+cos^ntheta, prove...

    Text Solution

    |

  2. prove-that-1-cota-tana-sina-cosa-seca-cosec-2a-coseca-sec-2a-sinatana-...

    Text Solution

    |

  3. If x=asectheta+btantheta and y=atantheta+bsectheta ,prove that : x^2...

    Text Solution

    |

  4. If x/a costheta+y/b sintheta=1 and x/a sintheta-y/bcostheta=1 Prove...

    Text Solution

    |

  5. If cos e ctheta-sintheta=a^3,sectheta-costheta=b^3, Prove that : a^2b...

    Text Solution

    |

  6. Ifacos^3theta+3acosthetasin^2theta=m and asin^3theta+3acos^2thetasin^...

    Text Solution

    |

  7. If 3sintheta+5costheta=5, then show that 5sintheta-3costheta=+-3.

    Text Solution

    |

  8. If acostheta+bsintheta=m and asintheta-bcostheta=n , Prove that a^2...

    Text Solution

    |

  9. If costheta+cos^2theta=1, Prove that: sin^(12)theta+3sin^(10)theta+3si...

    Text Solution

    |

  10. If cottheta=15/8, then Evaluate ((2+2sintheta)(1-sintheta))/((1+costhe...

    Text Solution

    |

  11. Prove the trigonometric identities: (tantheta)/(1-cottheta)+(cottheta)...

    Text Solution

    |

  12. If sintheta+costheta=x , Prove that : sin^6theta+cos^6theta=(4-3(x^2-1...

    Text Solution

    |

  13. Prove the following identities: ((1+sintheta)^2+(1-sintheta)^2)/(co...

    Text Solution

    |

  14. Prove that (1-sintheta+costheta)^2=2(1+costheta)(1-sintheta)

    Text Solution

    |

  15. Prove the following identities: (sinA+secA)^2+(cos"A"+"c o s e cA")^2=...

    Text Solution

    |

  16. Prove the identity: (1+tanAtanB)^2+(tan"A"-tan"B")^2=sec^2Asec^2B

    Text Solution

    |

  17. Prove the following identities: 2(sin^6theta+cos^6theta)-3(sin^4theta+...

    Text Solution

    |

  18. Prove the following identities: tan^2A-tan^2B=(cos^2B-cos^2A)/(cos^2Bc...

    Text Solution

    |

  19. If costheta+sintheta=sqrt(2)costheta, show that costheta-sintheta=sqrt...

    Text Solution

    |

  20. If tantheta+sintheta=m and tantheta-sintheta=n , show that m^2-n^2= 4...

    Text Solution

    |